A Radiatively Cooled ADS Beam Window
Caroline F. Mallary
Advisor: Germano S. Iannachione
Physics MQP
April 26, 2007
Abstract
The purpose of this MQP is to examine candidate materials for the beam window of an
ADS reactor. ADS stands for Accelerator Driven System, a means of spallating atomic
nuclei to produce controlled nuclear fission, or to transmute existing nuclear waste into
species that are easier to handle. Due to the high power necessary for ADS accelerators,
the integrity of the accelerator’s beam window has been a concern. Progress has been
made on liquid-metal cooled ADS designs, especially in the ORNL and JAERI research
centers, but problems have become apparent, too. My project was to investigate potential
materials for an ADS beam window that can radiatively cool itself.
Section 0: Introduction
0.1 What is ADS?
Sustainable energy production has become an increasingly important issue in the world
today. The burning of fossil fuels has many environmental and political consequences,
and alternatives to them are being sought. While renewable sources such as wind and
wave power deserve attention, nuclear power is the only emission-less option that is
independent of location and environment. Traditional fission plants are not favored by
many people because of perceived problems with safety, and the long isolation time
required for reactor waste. ADS is a nuclear option that addresses both these issues.
ADS stands for Accelerator Driven System. In ADS, an accelerator is used to produce
some of the neutrons necessary for nuclear fission. Because these neutrons are not
produced by chain reaction, their production can be stopped at any time: No active
intervention is necessary to prevent them from being created. What this means is that the
chain reactions in an ADS core can never get out of hand, because they depend on the
accelerator to sustain them. An ADS core is sub-critical, and it can’t run on its own.
This addresses one of the biggest popular concerns about nuclear power. An ADS
reactor will never suffer accidental meltdown.
Because ADS can run on a sub-critical core, it can burn materials that are not currently
fissionable. Namely, it can burn the waste of other reactors (Fig. 1). There is a great deal
of energy stored in nuclear waste (Fig. 2). It is this energy that makes it so damaging to
the environment. ADS causes some of the energy stored in minor actinides and longlived fission products (MAs and LLFPs) to be released immediately. It can then be
capture in a power-generating plant, instead of a mountain. It is believed that 95% of
MAs and LLFPs can be transmuted, and that an ADS could process 250 kg of nuclear
waste every 300 days. ADS could reduce the geological storage time for nuclear waste
from millions of years to less than 500 years1. This lifetime is feasible for a geological
storage facility: Architects have been building structures that last this long for millennia.
Figure 1. Concept of a Power & Transmutation system for long-lived radioactive
nuclides by JAERI. From Y. Kurata, T. Takizuka, T. Osugi, H. Takano, JNM 301, 1,
(2002)
The mechanism by which the accelerator produces the needed neutrons is called
spallation. Ions, usually protons, are accelerated to extremely high energies (~1 GeV)
and aimed at a “target”. The target material may be chosen on several different criteria,
but the most important is having a large number of neutrons. Spallation is a fancy word
for smashing the target nuclei to bits. When the nuclei are smashed, dozens of neutrons
may be freed and continue on into the core. They must be moderated first, as some will
have very high energies. However, it is not necessary to thermalize them. An ADS
would most likely be fast-neutron reactor, because fast neutrons are not as easily
absorbed as thermal ones. This would ensure that more waste was burned than created.
Figure 2. Radioactive power from decay of fission products and actinides. This decaypower results from the waste of 1 mo. of operation of a 1000-MW power plant. Solid
curve is the sum of contributions of individual isotopes. From B.L. Cohen, Rev. Mod.
Phys 49, 1 (1977) via [2].
_____________________________________________________________________
Figure 3. Spallation. Hand-drawn.
Interest is ADS has been building quietly for a long time. There are two facilities already
built which focus on ADS. Both Oak Ridge Nat’l Laboratory (ORNL), and J-PARC in
Japan have beams online for this purpose. Oak Ridge’s Spallation Neutron Source (SNS)
has been operating since June 2006, and J-PARC’s spallation facility came online in
October 2006. J-PARC will begin work with minor actinides in its Transmutation
Experimental Facility in the near future. In Europe, the MEGAPIE beam at SINQ in
Switzerland is used for spallation experiments, but a fulltime European Spallation Source
has not yet been built
0.2 The Beam Window
Figure 4.
One of the window designs considered for SNS.
Note the domed central portion.
From Proceedings of the Particle Accelerator
Conference, ORNL team, 2003.
____________________________________________________________________
ADS is in the process of evolving, and one of the engineering problems thus far has been
the beam window. The ADS accelerator must be kept at high vacuum, and some
structure has to be responsible for keeping air and other gases out. The problem is that
this same structure must also allow the beam to get out. Very high proton fluxes are
necessary to produce enough neutrons to run a sub-critical fission reactor. One such
estimation, done in Section 5 of this report, requires a flux of 1017 protons per second,
each at 1 GeV. This amounts to a 16 MW beam. A beam like this is capable of melting
most things that are put in front of it, and does extensive radiation damage to whatever
remains solid.
Radiation damage to the window is not dealt with broadly in this report, because the
extent and form of it depends on many factors. These include nuclear and chemical
properties of the material itself, temperature at which irradiation occurs, characteristics of
radiation, and even spatial orientation of the crystals in the material. In short, it is
experimental work. One such experiment was done in conjunction with this report, and is
described in Section 6.
The main focus of this report is the mechanical properties of materials from which the
window could be made. It is hoped that a radiatively cooled window, which is run hot,
would be able to anneal much of the radiation damage done to it. This may be possible
because of the type of damage that can do be done to it. A brief overview of radiation
damage is given below.
Several different types of damage can occur. The crystal structure of the window is
damaged by the high-energy ions (protons) passing through it. The atomic dislocations
cause hardening and eventually embrittlement. This may be similar to the phenomenon
which causes overwrought metals to become work-hardened. Irradiation-swelling of the
material can also occur when dislocations result in large voids in the material, or
transmutation precipitates form bubbles in it. Transmutation products are an issue: The
protons may spallate or “side-swipe” the window nuclei themselves. They break
nucleons off the window nuclei, or even shatter them. Additional radiation damage then
occurs due to neutron bombardment, gammas, and free charged particles. In Oak Ridge’s
SNS, hydrogen and helium bubbles are common in used 2mm steel windows 3,4. This
causes them to be brittle. Sulfur, phosphorous, and other elements will also replace some
of the iron, and have a similar embrittling effect. The transmutations cannot be prevented
by running the window hot, but transmutation gases may be able to escape the window.
Additionally, a design in which the beam is split and sent through multiple windows
reduces radiation damage. If the windows are radiatively cooled, and therefore outside
the core, a multi-beam concept is more feasible than with some other schemes.
A common unit of radiation damage is dpa, or displacements per atom. I was unable to
determine why this unit is used, as it is material- and energy-specific, and physically
means nothing without the application of algebra. Additionally, this algebra has obscure
material properties as inputs. The eventual result of conversion is the number of incident
ions necessary to make one displacement likely. I was unable to determine how to use
dpa to express damage done by neutrons. Anyone wishing to know how to work with
dpa should consult [5], and be aware that (dE/dx)nuclear is equivalent to nuclear stopping
power times material density. Information on nuclear stopping powers can be found at
[6].
The mechanical properties of the window are a major issue, and it is the issue most
addressed in this report. The beam can deposit an incredible amount of heat into the
window, and it is necessary to get rid of this heat. There are several proposed schemes..
Windowless designs duck the issue entirely. In windowless designs, the spallation target
is right up against the accelerator vacuum. However, there may be problems with
evaporation of target material into the vacuum. This is especially true if a liquid metal
target is used.
Gas cooling, which was briefly considered when this project began, is probably unable to
remove heat from the window fast enough to be a primary cooling mechanism. It will be
seen later in this report that heat deposition in the window can be phenomenal. Over a
100,000 W may be put into a window less than a millimeter thick, if the beam is run
continuously. Most designs feature a pulsed beam, which allows some time for heat to
disperse.
In J-PARC and Oak Ridge, the solution to heat in the window is liquid-metal cooling.
This liquid metal is mercury in both cases. Lead-bismuth eutectic alloy has been
considered as well. Using liquid metal has some advantages. It is coolant for both the
window and the core, and it is the target as well. Being a liquid, target radiation damage
is not a concern: Neutron brightness can be maintained easily. Liquid metal ADS is
currently seen as the most promising design.
There are disadvantages to liquid metal, though. The proximity of the window to the
target increases radiation damage from neutrons. Liquid metal puts more pressure on the
window and is highly corrosive: Its contact with the window is chemically damaging.
This damage is exacerbated by conditions peculiar to ADS.
The pulsed beams in SNS and J-PARC are very intense. They cause instantaneous rates
of temperature change on the order of 107 K/s [7], though the window itself may be only
10 K above surroundings. This results in shock waves in the mercury. The shock waves
can tear voids into the mercury, a phenomenon known as cavitation. When these voids
collapse, they shoot high-pressure jets of liquid mercury at the window. Some of the
deep “pitting” caused by this can be seen in Fig. 5.
Figure 5. Pitting in an annealed 316LN window (SNS). From: J. Hunn, B. Riemer, C.
Tsai, JNM 318, pg. 102, (2003)
One more potential solution to heat in the window is radiative cooling. This is described
in the next section.
References for Section 0:
[1] Y. Kurata, T. Takizuka, T. Osugi, H. Takano. JNM 301, 1, (2002)
[2] K. Krane. Intro. To Nuclear Physics, Wiley, 1988
a means of spallating atomic nuclei to produce controlled nuclear fission, or to transmute
existing nuclear waste into species that are easier to handle.
[3] P. Vladimirov, A. Moslang, JNM 356, 1-3 (2006) p. 287-299
[4] R.L. Klueh, N. Hashimoto, M.A. Sokolov, P.J. Maziasz, K. Shiba, S. Jitsukawa. JNM
357, 1-3 (2006) p. 169-182.
[5] Lee, Hunn, Hashimoto, Mansur. JNM 278, 2-3 (2000) p. 266-272
[6] Isotopes Project, Lawrence Berkeley Laboratory: (get authors, dates)
http://ie.lbl.gov/interact/abs3c.pdf
[7] John R. Haines. Target Systems for the Spallation Neutron Source, PowerPoint
(2003)
+In-line References
Section 1.0: Radiatively Cooled Window - Description
This project is meant to demonstrate the feasibility of a radiatively cooled ADS beam
window.
Radiative cooling comes naturally to an object that is much hotter than its surroundings.
The formula for power emitted is:
P = a (T 4- ambient temperature4)
where P is power in Watts, T is the temperature of the object, and a is the emissivity of
the material. Emissivity is a unit-less number that is always less than 1. Emitted power
rises rapidly with increased temperature. Therefore, a radiatively cooled beam window is
run hot.
At elevated temperatures, metals lose strength and stability. At some point, the window
will no longer be able to hold back an atmosphere of pressure. Strength can be improved
by increasing thickness, but this also increases the amount of heating by the beam.
Designing a radiatively cooled beam window is therefore an optimization problem. A
particular window material with be able to tolerate the most proton flux at a particular
operating temperature and thickness.
Figure 1. Dynamics of a radiatively cooled beam window.
Section 1.1: Considerations
Heating by the beam is given by 1:
H  Fp  S(E 0 )  z    k
where
H  Heating, in Watts
Fp  Flux of protons through w indow, in protons / second
S(E 0 )  Stopping power of window material, for protons of specified energy,
in
MeV
proton * g/cm 2
  Density of window material, in g/cm 3
k  1.602 * 10 -13 Joules / MeV
z  Thickness of the window (average), in cm
This formula was adapted from one found in the Journal of Nuclear Materials, Volume
356, Issues 1-3, “Irradiation conditions of ADS Beam Window and Implications for
Window Material”. That formula gave the rate of heating in Watts per gram, and
appeared as: H  Fp * S(E 0 ) /  * k, which appears to have a units error. This version of
the formula is justified as follows:
Each proton that passes through the window will, on average, lose a certain amount of
energy to the window, heating it. This energy is described by the stopping power, S(E0),
used in the formula above.. Although it is being assumed here that the proton does not
actually collide with nuclear material in the window, it does pass through the window’s
electron cloud. The electron cloud exerts a pull on the proton, and some of the proton’s
energy is used to overcome it. For a 1 GeV proton, the energy lost to the window is
typically about 1-2 MeV/(g/cm2). This unusual unit becomes more understandable when
used in a formula.
For instance, a radiative steel window may be 0.0020 cm thick, and it has a standard
density of 7.8 g/cm3. So, one square centimeter of the window has volume of 0.0020
cm3. Its mass is (7.8 g/cm3)  (0.0020 cm3) = 0.016 g. That is, there are 0.016 grams of
material present in each square centimeter of the window, or 0.016 g/cm2.
The stopping power of steel is about 1.6 MeV/(g/cm2) for a 1 GeV proton1, 2. So, each 1
GeV proton loses (1.6 MeV/(g/cm2))  (0.016 g/cm2) = 0.026 MeV of energy to the steel
window.
If the proton flux is 1017 protons per second striking the window, then a total of
0.026  1017 MeV is deposited in the window each second. This is equivalent to 420
Joules per second, or 420 Watts.
The stopping power of a material may be calculated using a semi-empirical formula
provided by the Isotopes Project of Lawrence Berkeley Laboratory2. The stopping power
decreases when the proton beam’s energy is increased. At the energies relevant to ADS,
the stopping power comes almost entirely from the material’s electron cloud. There is a
nuclear component of stopping power, but it is negligible, and left out of the formula
below.
2
The formula is:
2

 ln E 
 ln E 
 E  0.6022
S e   A9  A10 
 10 3
  A11 
  A12 
 
M
 E 
 E 
 ln E 

Here, M is the window material’s atomic mass, in amu, E is proton energy in keV, and
the An coefficients are empirical constants which are listed on the site by proton energy
and the material which the protons strike. The complete table of An is available there2.
An abbreviated version, containing only elements likely to be of interest for an ADS
beam window, is on the next page.
Table 1.
Material
Z
M
A9
A10
A11
A12
(amu)
E
Stopping Power
(keV)
(MeV/(g/cm2))
Titanium
22
47.88 7.50E-02 2.96E+03 -5.56E+05 1.81E-07
106
1.62
Vanadium
23
50.94 8.17E-02 3.05E+03 -4.62E+05 1.81E-07
106
1.62
Chromium
24
52.00 8.17E-02 3.15E+03 -5.51E+05 1.89E-07
106
1.61
Iron
26
55.85 8.79E-02 3.35E+03 -6.06E+05 2.01E-07
106
1.60
Nickel
28
58.69 9.44E-02 3.53E+03 -6.12E+05 2.10E-07
106
1.62
Zirconium
40
91.22 1.33E-01 4.88E+03 -1.01E+06 2.91E-07
106
1.46
Niobium
41
92.91 1.36E-01 4.97E+03 -1.02E+06 2.95E-07
106
1.46
Molybdenum 42
95.94 1.36E-01 5.17E+03 -1.42E+06 3.24E-07
106
1.45
Tantalum
73
180.9 2.31E-01 7.93E+03 -2.20E+06 4.74E-07
106
1.25
Tungsten
74
183.9 2.28E-01 8.16E+03 -2.95E+06 5.21E-07
106
1.24
Rhenium
75
186.2 2.35E-01 8.11E+03 -2.44E+06 4.93E-07
106
1.24
It can be seen that higher Z elements trend to lower stopping powers. The actual best
material for the window is likely to be an alloy, due to the improved mechanical
properties available. In cases where one element is predominant, such as carbon steel, it
is sufficient to use the stopping power of the predominant element, in this case, iron.
High-carbon steel is only about 2% carbon, and ignoring carbon’s contribution only leads
to a loss of one significant digit. Likewise, the stopping power of an alloy containing
similar-Z metals can probably be estimated by inspection. In other cases a weighted
average can be used to find the stopping power of the alloy.
While the higher-Z materials have lower stopping powers, they also have higher
densities. Density is one of the factors used to determine how fast the window heats up.
The higher densities of the higher-Z materials limit the benefit of their lower stopping
powers.
The window’s tensile strength at operating temperature must be sufficient to hold back an
assumed 1 atmosphere (0.101325 MPa) of pressure. The calculations to determine if this
is possible are demonstrated below.
Tensile strengths of any sort are given in units of Force/Area. It is therefore necessary to
determine how the atmosphere exerts force on the window, and on what area it is exerted.
While the entire window is responsible for keeping the atmosphere out of the accelerator,
the greatest load is on the edges of the window, where it is supported. If the edges can
hold up, the rest should, too.
A hemispherical window design allows for the best support. The increased surface area
of a hemisphere compared to a circle does not increase total force on the window. This is
because the radial components of force cancel out. The component of force pushing the
window back into the accelerator is proportional to the accelerator’s circular opening.
The radial atmospheric forces do serve a function, however: They allow the window to
hold its shape, much like a balloon.
Figure 2. A hemispherical window.
3
The total force on the supporting edge of the window is given by:
Forcetotal  R 2  (Ambient Pressure )
4
The area of the supporting edge is:
Perimeter Area  2R  (Thickness of Edge )
The thickness of the window at the edge may be slightly greater than the thickness of the
window at the center. This is the case at Oak Ridge, where the edge is about 150% the
thickness of the center. The radius of the window is in the vicinity of 10 cm.
5
The total amount of pressure that the window’s edge must hold back is:
Load 
Force total
Perimeter Area
If the tensile strength of the material is greater than the load, then the window will hold,
at least for a short time. In practice a safety factor would be put into the thickness.
Section 1.2: Assumptions for Optimization
In order to determine the best candidate materials for a radiatively cooled window, alloys
based on 12 elements were examined. The maximum proton flux that a window of each
alloy could withstand was determined based on the following assumptions:
1. The window is in all cases 10cm in radius, and must hold back 1 atmosphere
(0.101325 MPa) of pressure. The load-bearing edges of the window are 1.5 times
thicker than the window’s center. This is similar to the windows used in Oak
Ridge’s SNS. The window is hemispherical, but the amount of inward force on it
is proportional to the amount of it facing outwards, so the window may be
approximated as a flat disc. Material densities used are room temperature
densities, on the assumption that any decrease in density at high temperature will
come with an equivalent increase in window thickness.
2. The ambient temperature is 300K, and the only source of heat in the window is
the 1 GeV proton beam. Depending on reactor design this may or may not be a
reasonable assumption: According to models generated by P. Vladimirov and A.
Moslang for their 2006 article in the Journal of Nuclear Materials1, one sixth of
the heating may come from gamma rays and another 0.5% from neutron
bombardment. However, this estimate is for an ADS design in which the window
is in direct contact with the liquid-metal target. Here, heating by the reactor, and
cooling by convection, are assumed to be negligible: The window is outside the
nuclear core. It is assumed the window may be blackened so that it radiates 90%
as much power as a blackbody of the same temperature. The window radiates
from both its inside and outside surfaces; however, only the amount of it facing
directly inward or outward radiates effectively. For radiative purposes, the
window may again be approximated as a flat disk. All elemental stopping
powers are calculated based on data provided by LBNL’s Isotopes Project2, and
all alloy stopping powers are taken to be a weighted average of their major
constituent elements.
3. The beam is operated in continuous mode, so the cyclic fatigue properties of
the materials are not relevant. The beam has a “uniform” profile, in that it causes
uniform heating. In fact, a uniform profile will not cause uniform heating,
because the protons near the edges of the hemispherical window see more
material in their way. The flux per square centimeter given in the tables below is
the maximum flux that can be tolerated at the center of the window, and total flux
can be generated from it using these geometric considerations. Total flux is about
163 times the central flux. The calculations are done in Section 3. Beam current
in mA is gotten by multiplying total flux by 1.602  10-16.Coulombs. Radiation
damage from the beam or backscattered neutrons is not addressed quantitatively
here.
In a radiatively cooled design, the window must emit as much power as it absorbs as heat
from the protons. This is necessary for it to remain in equilibrium. Radiative designs
lend themselves to hot windows: If the window were at 300K like its surroundings, its
net emission would be 0 W. For each candidate material, there is an ideal range of
operating temperatures, where the proton flux is maximized, the window is thick enough
to be strong and durable, and thermal equilibrium is maintained.
Recall that the formula for heating is:
H  Fp  S(E 0 )  z    k
where
H  Heating, in Watts
Fp  Total flux of protons through w indow, in protons / second
S(E 0 )  Stopping power of window material, for protons of specified energy,
in
MeV
proton * g/cm 2
  Density of window material, in g/cm 3
k  1.602 * 10 -13 Joules / MeV
z  Thickness of the window, as seen by incoming protons, in cm.
Fp is not actually known, because the flux is not uniform, and z varies considerably
(Assumption 3). However, it is assumed that the beam profile can be manipulated so that
these factors offset each other, making Heating uniform. This makes it unnecessary to
know either Fp or z at the moment. The flux per square centimeter, fp, is presumably
maximum at the window’s center, so if that can be found, we will be able to determine
what the rest of the window can tolerate. A conversion from the central flux per square
centimeter, fp0, to total flux, Fp, is done in detail in Section 3. Under the assumptions
made there, Fp 163 fp0.
Because this is a radiatively cooled design, Heating must equal Emitted power. The
maximum flux fp0 through a square centimeter at the center of the window is then given
by:
fp0 = Emitted / ( S(E0)  z    k  R2 )
where z is now specifically the thickness at the center of the window, and 1/R2 is a
conversion factor from *Fp*, the total flux the window would experience if it were a flat
disc of z thickness, to fp.
There are now two different unknowns to deal with: z and Emitted. Emitted power, by
Assumption 2, is a function of temperature (and window radius, a constant here), and z is
a function of material strength (also radius and ambient pressure, both constant here).
Both temperature and material strength may be regarded as independent variables. This
may seem backwards: Temperature is high because of the protons, and materials lose
strength because of high temperatures. However, material strength is a bounding
condition: The window has to be strong enough, or it serves no purpose. Strength
dictates the beam power possible. Temperature is also “independent”, in that it is
plugged into a formula to determine Emitted power, with no explicit relation to strength.
_______________________________________________________________________
Section 2: Materials - Maximum Possible Flux
In materials science, there is seldom an exact formula for how strong a material is under
different conditions. Fortunately, there is a large amount of data available on the subject.
In each of the 12 alloy-bases studied, data sheets were found that gave the tensile strength
of materials at high temperatures. Tensile strength tends to degrade if materials are kept
at elevated temperatures for a long time, and where possible, long-term tensile strengths
were used.
Below is a sample table that shows which formulas were used in calculating the
maximum flux each alloy can tolerate. These formulas are derived from the assumptions
described in Section 1.
T(K)
UTS (MPa)
Input
Input
Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
0.90×2×σ×πR2×
(T4 – (300K)4)
_Safety×R×atm_
2×S(E0)×1.50
_Emitted_
×S(E0)×z×πR2
T is Temperature in Kelvin, UTS is Ultimate Tensile Strength in megapascals (sometimes
given for long times at temperature), W is Watts, σ is the Stefan-Boltzmann constant, R is
the window radius, and atm is the ambient pressure. All these formulas must include the
necessary conversion factors so that units agree. Very often raw data was given in units
of kpsi (thousand lb. / in2), and had to be multiplied by 6.892 to convert it to MPa.
Similarly, temperatures were given in several scales. Density and stopping power for
each material are given in the blurbs near its respective table. Beam current in mA can be
obtained from proton flux/cm2 at the center by multiplying by:
1.602×10-19 C/p×1000 mA/A × (163.1=Total flux/(flux/cm2))
For each alloy-base, an effort was made to find the most suitable alloy for an ADS beam
window. In some cases, such as vanadium-based alloys, data was limited, in others, such
as steel, there was so much data a thorough search would be outside the scope of this
project.
The alloys examined were found to fall into two categories: Low temperature, lower
beam-current alloys, and refractory alloys. The low-current alloys have the six
atomically lightest bases. They have a distinct advantage, in that they may be run in air
at the relevant temperatures. Their ideal operating temperatures, where the most proton
flux could be tolerated, were no higher than 650C, and they typically tolerated fluxes on
the order of 1014 protons/cm2/s, or several mA total beam current. Because these protons
are at 1 GeV the corresponding beam power would be the same number of MW as mA.
(e.g., 7.5 mA implies 7.5 MW) This may be sufficient for a power-generating ADS
reactor.
In this section, calculations are done to find maximum total proton flux possible. The
maximum tolerable flux is inversely proportional to window thickness. In some cases,
especially among the refractory metals, the max flux may be much higher than is
necessary for a power-generating ADS, and the window thinner than is easily fabricated.
For example, an Inconel-718 window can cope with 73.3 mA of beam current at 0.012
mm of center thickness. This is about the same thickness as light aluminum foil. Inconel718 is difficult to machine, and a decent-size power-generating ADS may only need 16
mA of beam current. This window would be better if it were:
(73.3mA / 16 mA)  0.012 mm = 0.055 mm thick, with 16 mA of beam current
There is now a factor of 4.58 safety in the window’s thickness, in addition to the factor
of 4 safety that was present in this window before.
In Section 4, I will give window thicknesses and relative strengths of some windows
whose beam current restricted to 16 mA. In the Power Generation Section, I will justify
the assumption that a 16 mA beam can sustain a decent-size (660MW) power plant.
The refractory alloys can generally cope with 10 times as much beam current as the lowtemperature alloys, or be 10 times thicker for the same current. This thickness, aside
from making fabrication easier, reduces the air-pressure stress on the window.
Unfortunately, actual air cannot be used in the reactor, because all the refractory alloys
burn in oxygen at operating temperatures. It may be possible to run them in a nitrogen
atmosphere, doped with a small amount of hydrogen to stick to any oxygen that leaked
in. Helium is another possibility, but is more likely to leak through the window itself.
The refractory alloys may also cope with radiation damage better, as higher temperatures
may allow transmutation gasses to escape more easily, and some radiation damage may
anneal away. However, since the refractory alloys get their high-temperature strength
from structural resistance to heat, this requires experimentation.
The advantages that may be offered by refractory alloys must also be balanced against the
fact that it may be more difficult to blacken them to emit properly. The requirements of
blackening are somewhat less stringent because hot metals emit at a higher percentage of
blackbody to begin with.
Section 2.1: Low-Temperature Alloys
1. Aluminum (Z=18).
Aluminum H16, H18, and 2014-T6 were examined, and 2014-T6
(90.4 - 95% Al, 3.9 - 5% Cu, 0.2% Cr max, 0.7% Fe max) was found to have the best
properties of these alloys. Aluminum alloys are inferior to other low-current alloys for
ADS purposes. However, they are suitable for other types of accelerators: The MITBates linear electron accelerator has a window of 0.05mm thick, Teflon-coated aluminum
foil. (This accelerator also makes use of a concept that could be useful in ADS: There
are several incomplete windows inside the accelerator, which are differentially pumped
so as to make a transition from 10-9 atmospheres in the main accelerator to 10-5
atmospheres behind the aluminum window. Source: Jan Vanderlaan, MIT-Bates.)
T(K) UTS (MPa) 10,000 hr Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
300
483
0
0.007
0.00E+00
366
415
32
0.008
1.12E+14
422
145
76
0.023
9.30E+13
477
101
141
0.033
1.21E+14
533
63
233
0.054
1.24E+14
589
29
359
0.117
8.83E+13
Table Set 1. Density = 3.96g/cc, Stopping Power= 1.75 MeVcm2/g. Values obtained
and converted from the image above. The best thickness for this window is 0.054 mm,
about the thickness of heavy-duty aluminum foil. There is a maximum total beam current
of 3.24 mA, or 3.24 MW beam power for 1 GeV protons. One beam like this might
sustain a small power plant at full power (see Power Generation Section), but not a large
one. Although 10,000 hr strengths of Al 2014-T6 were used, the lifetime has little
tolerance for error at the best operating temperature of 533K ( = 260C = 500F).
Source: W.F. Kehler. Aluminum, 1980
2. Titanium (Z=22).
Various Titanium alloys were examined; only “beta” titanium alloys were found
to have good strength. Of these, Crucible Beta III (Ti-11.5%Mo-6%Zr-4.5%Sn)
was found to have the best properties at temperatures below 730F. Titanium alloys are
superior to Aluminum alloys in terms of the flux they can tolerate.
T(K)
533
589
644
700
Creep Stress (MPa)
100 hr
896
793
517
159
Emitted Power Center Thickness (mm) Max Proton Flux/cm2
(W)
233
0.015
3.77E+14
359
0.017
5.14E+14
526
0.026
4.91E+14
742
0.085
2.13E+14
Table Set 2. Density = 5.09g/cc, Stopping Power= 1.6 MeVcm2/g. Values obtained
and converted from the image above. Because only short lifetime data was available, a
safety factor of 4 was put into the thickness of the window, which reduced the Max
Proton Flux by a factor of 4. As this material will only creep 0.16% in 100 hours without
the safety factor (see upper left of image), a reasonable lifetime can be expected from this
window if radiation damage can be tolerated. The best center thickness is 0.017 mm
(similar to standard aluminum foil), at an operating temperature of 589K ( = 316C =
600F). Proton flux can be four times higher than through the Aluminum-base window,
with a maximum total bean current of 13.4mA. Source: ASM Online Data Sheets.
3. Vanadium (Z=23).
Data on Vanadium-based alloys was somewhat incomplete; no very long lifetime
stresses were available. Of the alloys for which 100hr rupture data was available, V40%Ti-5%Al-0.5%C was found to have the best properties. Based on a graph on pg.93
of The Metallurgy of Vanadium, an alloy with a somewhat lower percentage of titanium
may perform better. The 0.5%C increases strength, as does the 5% aluminum, which
gives the alloy better stress-rupture properties than an equivalent amount of chromium.
Pure Vanadium is a hard material, like Chromium. Calculations indicate that if sufficient
lifetime and fabricability can be demonstrated, then Vanadium-based alloys could be a
good choice for a lower-current, air-operated window, as this alloy is able to tolerate a
beam current of 38.7 mA.
T(K)
673
773
873
UTS (MPa) 100 hr
Rupture
920
772
283
Emitted Power Center Thickness (mm) Max Proton Flux/cm2
(W)
632
0.015
9.96E+14
1119
0.018
1.48E+15
1836
0.048
8.89E+14
Table Set 3. Density = 5.3g/cc, Stopping Power= 1.62 MeVcm2/g. Values obtained
and converted from the image above. Because only short lifetime data was available, a
safety factor of 4 was put into the thickness of the window. The best center thickness is
0.018 mm, at an operating temperature of 773K ( = 500C = 782F), and a maximum
total beam current of 38.7 mA. This proton flux is almost 3 times higher than through the
Titanium-base window. Source: Rostoker. The Metallurgy of Vanadium, 1958.
4. Chromium (Z=24).
Chromium is more typically found as an additive than a base in alloys. It is
particularly good at improving corrosion resistance, such as the “stainlessness” of
stainless steel. Only one majority-chromium alloy was found with sufficient data to
analyze it as a window material, a 50Cr-50Ni alloy. Stress-rupture-data for 1,000 hrs was
used with a safety factor of 2 in the window thickness. This translates to half as much
stress and proton flux. Because halving the stress tends to extend the window lifetime by
a factor of about 10 (see below), this window may last 10,000 hrs. This alloy is
somewhat inferior to Titanium Crucible Beta III, but may improve if used at lower
temperatures.
T(K) UTS (MPa) 1,000 hr Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
922
69
2290
0.098
3.66E+14
977
41
2901
0.163
2.78E+14
1033
24
3625
0.280
2.03E+14
1089
17
4476
0.392
1.79E+14
Table Set 4. Density = 7.92g/cc, Stopping Power= 1.6 MeVcm2/g. Values obtained
and converted from the image above. The best thickness for this window, based on the
data available, is 0.098mm, which in this material may be thick enough to make it rather
stiff. The best temperature is 933K (= 649C = 1200F) with a maximum total beam
current of 9.6mA. There is a safety factor of 2 in window thickness, which may extend
lifetime to 10,000 hrs. Lower operating temperatures may allow for thinner windows
and better performance. This window has similar flux tolerance to Titanium Crucible
Beta III, but removes more energy from the proton beam. Source: ASM Online Data
Sheets.
5. Iron (Z=26).
There is an immense variety of steels, and extensive documentation on their
properties. Because of this, a full survey of steel types is outside the scope of this project.
The familiarity of steel makes it attractive as a window material: The most suitable steel
found can tolerate 85% as much proton flux as the best Vanadium alloy, and has stress-
rupture data available to 100,000 hrs. (In actual ADS conditions, this lifetime would be
significantly shortened by radiation damage, but that is outside the scope of this section.)
Steel is also much less susceptible to fatigue than other metals, making pulsed-beam
operation more viable. Pitting-resistant 316 LN steel is in use at the liquid-metal-target
window at Oak Ridge’s pulsed SNS3, and the low-activation steel F82H has been
considered by researchers at Switzerland’s SINQ4. No high-temperature tensile data for
F82H could be found, although data for type 316 was available. For a radiatively cooled,
solid target window, it was found that the steel Sanicro 31HT was slightly superior to
type 316 (Eastern 316, data from ASM Online Data Sheets). This difference may
evaporate if the higher nickel content of 31HT is found to lead to premature
embrittlement, so data for both steel types has been provided in the tables below. The
steels Enduro HCN, Enduro 317 and Sandvik 253 MA were also examined, but were not
as good as 316 or 31HT.
Type 316 (Eastern): 10-14Ni, 16-18Cr, 2-3Mo, max 2Mn, max 1Si, max 0.08C, max
0.045P, max 0.30S. Density = 8 g/cc. Maximum total beam current is 27.2mA.
T(K) UTS (MPa) 10,000 hr Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
1% Creep
811
167
1360
0.020
1.04E+15
866
125
1780
0.027
1.03E+15
922
88
2290
0.039
9.21E+14
977
54
2901
0.062
7.26E+14
1089
19
4476
0.175
3.97E+14
________________________________________________________________________
Type 31HT (Sanicro): 30-35Ni, 19-23Cr, 0.15-0.60Al, 0.15-0.60Ti, max 1.5Mn, max
1Si, max 0.75Cu, max 0.10C , max 0.015P, max 0.015S. Density = 8.1 g/cc.
Maximum total beam current is 28.4mA.
T(K) UTS (MPa) 100,000 Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
hr Rupture
866
134
1780
0.025
1.09E+15
922
85
2290
0.040
8.94E+14
977
56
2901
0.061
7.40E+14
1033
35
3625
0.096
5.82E+14
1089
23
4476
0.149
4.65E+14
Table Set 5. Stopping Power= 1.6 MeVcm2/g in both cases. Lower operating
temperatures may give the metal some better characteristics, but higher temperatures may
give it higher radiation tolerance, and the thicker windows may be easier to fabricate.
This matter requires more investigation, as it has been found that irradiation temperature
has a significant effect on the form of radiation damage in some steels4. The best
thickness for the Type 316 window, based on the data available, is 0.020mm, with a
maximum total beam current of 27.2 mA and an operating temperature of 811K ( =
538C = 1000F),. The best thickness for the Type 31HT window, based on the data
available, is 0.025 mm, with a maximum total beam current of 28.4 mA and an operating
temperature of 866K ( = 593C = 1100F). Note that 316’s strength data is for 1% Creep
in 10,000 hrs, while 31HT’s data is for rupture in 100,000 hrs. These windows do not
have flux tolerances as high as that of the best Vanadium alloy, but are better studied and
have more reliable lifetime data. The thinnest of these windows is similar in thickness to
aluminum foil, the thickest is somewhat stiff. Source: ASM Online Data Sheets.
6. Nickel (Z=28).
.Unfortunately, extensive data could not be found on the most interesting Nickelbase alloy examined, Inconel-718. Inconel-718, should its lifetime prove sufficient, can
tolerate more flux than the best Vanadium alloy (nearly twice as much, if Inconel-718’s
long-term strength is assumed to be ¼ of its short-term strength at relevant temperatures).
Inconel-718 is the window material being used in a 1MW pulsed beam at the liquid-metal
J-PARC in Japan5. Inconel-718 may contain up to 1% cobalt. It was not determined if
the cobalt can or should be removed from metal used in a beam window.
One potential problem with this and other nickel alloys is that they are very hard,
and the window thicknesses which allow them the highest flux are no thicker than light
aluminum foil. Foils like this cannot be rolled, although it may be possible to use other
techniques such as powder-melting the window onto a mold. It its possible to make the
windows thicker, but then they will absorb more heat, and have similar considerations to
refractory windows. If fabrication of thin nickel-alloy windows is impractical then
windows of other materials are more attractive.
Other Nickel-base alloy studied include Kubota KHR48N, Udimet 901, MO-RE
40-MA, and Inco-Alloy 330. This is just a sampling, and there are likely to be others
worthy of consideration for the window. Of this sampling, none could tolerate as much
flux as the Inconel-718, but lifetime data was available. The Udimet and Kubota alloys
were nearly equal: Udimet came out ahead in the temperatures for which data was
available, but Kubota may be superior if allowed to operate at a lower temperature. Its
lifetime data is also more reliable.
Nickel alloys may function at greater than 650C (923K), but oxidation could
become a real issue.
Inconel-718: 50 – 55 Ni, 17 – 21 Cr, 17 Fe, 4.75 - 5.5Nb, 2.8 - 3.3 Mo, 0.65 - 1.15 Ti,
0.2 - 0.8 Al, Max 1 Co, Max 0.35 Si, Max 0.3 Cu, Max 0.08 C, Max 0.015 S, Max
0.015 P, Max 0.006 B. Density = 8.19 g/cc, Stopping Power= 1.62 MeVcm2/g.
There is a safety factor of 4 in the window’s thickness, reducing the flux by the same
factor. This is because of the lack of lifetime data. Maximum total beam current is
73.3mA, corresponding to a beam power of 73.3MW. Source: matweb.com.
T(K)
300
923
UTS (MPa) Short- Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
Term
1375
0
0.010
0.00E+00
1100
2301
0.012
2.81E+15
________________________________________________________________________
Udimet 901: 42.0Ni, 36.0Fe, 13.0Cr, 5.6Mo, 2.9Ti, 0.2Al, 0.15B, 0.03C, max 0.1Mn,
max 0.1Si. Density = 8.26 g/cc, Stopping Power= 1.60 MeVcm2/g. There is a factor
of 2 safety which is likely to extend the lifetime past 10,000 hrs. Flux tolerance
peaks near 650C (922K, 1200F), with a window thickness of 0.013 mm. Maximum
total beam current is 69.8mA. Source: ASM Online Data Sheets.
T(K) UTS (MPa) 1,000 hr Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
Rupture
811
772
1360
0.009
2.34E+15
922
524
2290
0.013
2.67E+15
977
365
2901
0.018
2.36E+15
1033
207
3625
0.033
1.67E+15
1089
83
4476
0.082
8.24E+14
________________________________________________________________________
Kubota KHR48N: 45 – 50 Ni, 25 – 30 Cr, balance Fe, 4.0 – 6.0 W, 0.4-0.6 C, max 1.5
Mn, max 1.5 Si, max 0.03 S, max 0.03 P. Density = 8.03 g/cc, Stopping Power= 1.59
MeVcm2/g. No safety factor is needed; stresses used are the minimum at which
rupture can occur after 10,000 hrs, and are not much higher than the average
stresses for rupture after 100,000 hrs. (Note, however, that these are extrapolated
values; see source image below.) Flux tolerance may be higher at lower
temperatures, for which there was no data. Maximum beam current for available
data is 32.7mA. Source: ASM Online Data Sheets.
UTS (MPa) min
Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
10,000 hr Rupture
1033
74.6
3625
0.045
1.25E+15
1144
38.5
5466
0.088
9.7E+14
1255
17.4
7928
0.194
6.36E+14
T(K)
Table Set 6. Inconel-718 is the best of all the low-current, air-operated window
materials if it has sufficient lifetime and can be fabricated. J-PARC’s spallation neutron
source, whose first beam came on line in late 2006, will be able to give data on this
material’s behavior when exposed, long term, to beam irradiation: Its window is made
from Inconel-718.
Many other Nickel-based alloys are promising. An advantage of the Kubota
KHR48N alloy is that data shows it has decent flux tolerance even when the window is
thick and stiff. The stress-to-rupture in a minimum of 10,000 hrs is close to the stress-torupture in an average of 100,000 hrs.
7. Zirconium (Z=40).
Zirconium which has been purified of Hafnium is known as “reactor grade”. Its
known suitability for such environments makes it worth looking at. Zirconium is not as
strong at elevated temperatures as some of the other metals examined.
T(K)
773
873
1073
1273
1089
UTS (MPa)
230
150
27
10
8
Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
1119
0.059
3.97E+14
1836
0.090
4.25E+14
4224
0.500
1.76E+14
8394
1.351
1.29E+14
15068
1.689
1.86E+14
Table Set 7. Zr-2.5Nb: Density = 6.53 g /cc, Stopping Power = 1.46 MeVcm2/g. This
alloy has its flux peak between 500 and 600C, and a thickness of 0.06 to 0.09 mm.
Maximum total beam current is 11.1 mA at 600C = 873K. Uncertainties are introduced
by the uncertainty in strength (UTS), which is as high as 50 MPa due to the difficulty of
“eyeballing” values from the logarithmic graph above. This is exclusive of uncertainties
in the measured strength, which, as with most metals examined, is seldom mentioned and
may be unknown. Source: Rodchenkov & Semenov. High Temperature Mechanical
Behavior of Zr-2,5 % Nb Alloy, SMiRT Conference, 2003.
Section 2.2: Refractory Alloys
The image below is from the NASA Technical Note Stress-Rupture and Tensile
Properties of Refractory-Metal Wires at 2000F and 2200F (1093C and 1204C) by
Petrasek and Signorelli, Lewis Research Center, 1969. This document made a detailed
study of many of the alloys also examined in this section. The purpose of the document
was to find suitable wires to act as reinforcing fibers in superalloy composites. Although
examining such fiber-reinforced materials was outside the scope of this project, they
ought to be considered for a radiative ADS window due to their higher strength. A
downside of composite materials is the heating irregularities they may introduce.
NASA Graph.
Although refractory alloys cannot be run in air, the entire reactor need not be in an inert
atmosphere. It may be possible to put an extremely thin, non-pressure-bearing window
some ways in front of the refractory window for the sole purpose of keeping a bubble of
inert gas in front of the window. This would require more examination. A similar
dummy-window could be used to keep mercury vapor away if a liquid-metal target were
being used.
8. Niobium (Z=41).
Niobium, sometimes known as Columbium, is considered the first of the
refractory alloys. Its strongest alloys, however, contained other refractory alloys. The
best such alloy in terms of high temperature mechanical properties was a Molybdenum
and Zirconium–modified ternary alloy, containing about 70% Nb, 20% W, 7% Ti, and
3% Mo. The Zr is a 1% addition that is important for strength, but it is not known which
other element(s) were reduced to make room for it. Because density data was not
available for this alloy at the time of writing, the density of the alloy Nb-28Ta-10W (also
known as FS-85) was used in calculations instead. FS-85 is examined here as well, and is
shown on the NASA Graph above.
Niobium is known to irradiation-harden: Yield stress may be increased by 30%
when irradiated to 1020 neutrons/cm2 at 20C and then annealed at 200C. This increase
in hardness, and corresponding increase in both strength and brittleness, was looked for
in Vanadium in the Experimental section of this report.
Source: Miller. Tantalum and Niobium, New York Academic Press, 1959
Source: Sisco (ed.). Columbium and Tantalum, Wiley, 1963
FS-85: 72 Nb, 28 Ta, 10 W. Stopping Power = 1.34 MeVcm2/g. Short-term
strength data was available for this alloy on matweb.com, for room temperature and
for 1588K ( = 1315C = 2400F). A safety factor of 4 was inserted into thickness to
make up for the lack of long-term data there. This may, based on NASA’s graph for
2200F, extend the lifetime past 1,000 hrs and possibly past 10,000 hrs: The
material’s 2400F short-term strength is equivalent to 23 kpsi, and it is only being
stressed at a quarter of that. The material’s 2200F, 1,000-hr strength is about 18
kpsi. This window can tolerate 92.0 mA of beam current.
UTS (MPa) Short- Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
Term
300
580
0
0.023
0.00E+00
1588
160
20364
0.084
3.52E+15
T(K)
Nb-7Ti-20W-3Mo-1Zr: Stopping Power = 1.43 MeVcm2/g. There is a safety factor
of 4 in this window due to lack of lifetime data. The density of FS-85 was used, but
Stopping Power was, as usual, a weighted average of the elemental Stopping Powers.
As the calculations stand, this window can tolerate a maximum flux of 126 mA.
Source: Sisco (ed.). Columbium and Tantalum, Wiley, 1963
T(K)
1273
1373
1473
1573
1673
UTS (MPa)
517
414
317
234
145
Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
8394
0.026
4.39E+15
11368
0.033
4.76E+15
15068
0.043
4.84E+15
19604
0.058
4.65E+15
25092
0.093
3.68E+15
Table Set 8. Density used for both alloys is 10.16 g/cc, the density of FS-85. The MoMOD + 1% Zr alloy appears to be the best of the Niobium alloys, but there is some
uncertainty in its density and lifetime. The data for FS-85 is more reliable. Other alloys
examined included Cb-22 and Cb-15W-5Mo-1Zr.
9. Molybdenum (Z=42).
Molybdenum-TZM, which contains 0.5% Ti and 0.08% Zr, was found to be a
very good refractory alloy. It may be in the recrystallized or stress-relieved (annealed)
condition. The recrystallized condition is about twice as strong but probably more prone
to embrittlement. It is very stable for long periods of time at wide ranges of high
temperatures. At 1200C, near where it tolerates the maximum flux, it is the most stable
of all alloys found ([10], pg. 14). However, it should be noted that oxidation can cause it
to fail catastrophically; that is, an oxygen leak would cause the window to burst rather
than erode. The distinction may or may not be trivial given the thinness of the window.
T(K)
300
700
922
1144
1366
1589
1811
1922
UTS (MPa)
1068
1137
841
744
620
379
172
103
Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
0
0.013
0.00E+00
743
0.012
8.43E+14
2291
0.016
1.92E+15
5470
0.018
4.06E+15
11152
0.022
6.91E+15
20397
0.036
7.72E+15
34454
0.078
5.93E+15
43727
0.131
4.51E+15
Table Set 9. Moly-TZM: Density = 10.16 g /cc, Stopping Power = 1.45 MeVcm2/g.
There is a factor of 4 safety which may be excessive given the stability of Moly-TZM at
high temperatures. The maximum flux shown on this table occurs at 1589K = 1316C =
2400F, but it is probably almost as high if not higher at 2200F, for which data was not
available from the source used for the rest of the table. This window can mechanically
tolerate up to 202 mA. Other alloy examined included binary Molybdenum-Rhenium
alloys. Source (Image & Data): ASM Online Data Sheets.
10. Tantalum (Z=73).
Tantalum, while strong, is unstable at high temperatures. It loses strength rapidly
if held at elevated temperatures for a long time. Because of this, Tantalum-based alloys
were deemed unsuitable for use in an ADS beam window.
Image Source: ASM Online Data Sheets.
T(K)
1073
1273
1473
1673
1873
UTS (MPa)
469
345
234
172
110
Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
4224
0.029
1.39E+15
8394
0.039
2.04E+15
15068
0.058
2.49E+15
25092
0.078
3.05E+15
39434
0.123
3.06E+15
Table Set 10. Ta-10W: Density ~16.7 g/cc, Stopping Power = 1.25 MeVcm2/g. This
is the alloy for which the table above gives data. Since density data was not available for
this alloy, pure density was used in calculations, so flux estimations are probably
optimistic. There is a factor of 4 safety, but it may be insufficient unless the 10% W
significantly improves stability. The maximum flux tolerated, according to calculations,
is 80 mA. Data Source: cabot-corp.com
11. Tungsten (Z=74).
Tungsten was one of the more interesting refractory alloys. Thoriated tungsten
(2% ThO2) is used in car headlights because of its good vibration resistance. Although
Thorium can become fissile, this is probably not relevant, as the proton beam is capable
of spallating even very stable elements like 56Fe. NASA deemed thoriated Tungsten to
be the best material for its wires in the study referred to previously [10]. It found that W2ThO2 was more stable than Rhenium-containing Tungsten alloys at high temperatures..
Alternately doped “non-sag” Tungsten, which is use in standard incandescent bulbs and
contains 60-200 ppm of Potassium, has good properties as well. This is because the
Potassium forms small bubbles which add stiffness to the material, a very similar
phenomenon to H or He embrittlement.
Doped Tungsten: Essentially pure. Source: Pink & Bartha (ed.). The Metallurgy of
doped/non-sag tungsten, Elsevier Applied Science, c.1989. Data is guessed from
Boser’s and Pugh’s data on image below and is somewhat uncertain.
T(K)
300
2250
2800
UTS (MPa)
1650
100
80
Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
0
0.008
0.00E+00
82148
0.135
5.05E+15
197052
0.169
9.69E+15
Thoriated Tungsten: 98W, 2ThO2. Source: Avallone & Baumeister (ed.). Marks'
Standard Handbook for Mechanical Engineers, McGraw & Hill, 10th Ed.
T(K)
1477
1922
2200
UTS (MPa)
276
207
172
Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
15251
0.049
2.58E+15
43718
0.065
5.55E+15
75038
0.078
7.95E+15
Table Set 11. Stopping Power and Density of pure Tungsten used in both cases, 1.24
MeVcm2/g and 19.3 g/cc, respectively. There is a factor of 4 safety in both cases.
Doped Tungsten may reach a maximum beam current of 253 mA, but must do this at a
very high temperature. In Section 4, conversions to a greater thickness and 16 mA (16
MW) beam are done for ideal operating temperatures. Doped Tungsten run at its ideal of
2800K would heat the window so much that it would start to cut noticeably into beam
efficiency. There is no real need to run a doped tungsten window this hot, unless it is the
only way to anneal radiation damage. The Thoriated Tungsten may be a better choice
and according to [10], it is very stable at least up to 1477K, where it can mechanically
tolerate 67.5 mA. The calculated maximum for WThO2 is 208 mA.
12. Rhenium (Z=75).
Of the more exotic refractories studied, which included Osmium and Iridium,
Rhenium was the only one for which sufficient data could be found. Rhenium is very
hard and very expensive, and of all 12 metals reported in this paper, it was the only one
which may be best in its unalloyed form.
T(K) UTS (MPa) 1,000 hr Emitted Power (W) Center Thickness (mm) Max Proton Flux/cm2
Rupture
1873
14
39434
0.490
6.13E+14
2473
8
119897
0.891
1.03E+15
Table Set 12. Pure Rhenium: Density = 21.03 g/cc, Stopping Power = 1.24 MeVcm2/g.
There is a factor of 2 safety in the window thickness which will hopefully extend the
mechanical lifetime past 10,000 hrs. Data is taken from the graph above; it is visually
extrapolated for 1873K = 1600C. At this temperature it will take a beam current of
exactly 16 mA, enough to run an ~660MW power plant. (See Power Generation
Section). It is capable of a 26.7 mA (26.7 MW) beam, which is less efficient: It loses
about 0.5% of its power to the window. Lifetime data for other temperature was not
found. Data Source: REMBAR.com
________________________________________________________________________
Section 3: Total Flux Calculations
To convert from flux per square centimeter at the center of the window, fp0, to total
proton flux, Fp, assumptions must be made about the geometry of the window. It has
been stated that the window is 1.5 times as thick near its edge as at its center, that it is
hemispherical, and that it is being evenly heated by the protons. Since heating by the
protons is proportional to the thickness of window they must pass through, flux must be
reduced near the edge to account for greater thickness. This makes calculating total flux
through the window somewhat involved. In the calculations below, the perpendicular
thickness of the window, z(r), is assumed to increase linearly with r, so
z(10cm) = 1.5z(0cm). The thickness of the window that protons must pass through is
labeled s. At r = 0cm, s = z. The flux at r, fp(r), is inversely proportional to s, with a
constant of proportionality .
The Integrator program at wolfram.com (integrals.wolfram.com) was used to solve this
integral. A screen shot is below. The program took x as input instead of r, and the
constants at the front of the integral were left off.
Using the limits of integration x = 0 and x = 10, and returning the constants 2fp0 to the
front of the integral, the solution becomes Fp  163.1 fp0
Section 4: Materials - A 16 mA Beam and Thicker Windows:
Aluminum, Titanium, Chromium and Zirconium –based windows are all unsuitable for a
16 mA beam.
A V-40Ti-5Al-0.5C window can mechanically tolerate 38.7 mA at 0.018 mm of center
thickness and an operating temperature of 500C. This thickness includes a factor of 4
safety to compensate for the fact that only 100-hr rupture strengths were available. If the
beam were 16 mA, then this window could be 0.044 mm thick and still operate at 500C.
Assuming it was still hemispherical and 1.5 as thick at the edge, the safety factor would
be increased to 9.68 from 4 due to the greater thickness. (An additional factor of 2.37)
A 31HT steel can mechanically tolerate 28.4 mA of current at 0.025 mm of center
thickness and an operating temperature of 593C. This thickness includes no safety
because rupture strengths used are for 100,000 hrs. According to [1], operating at
temperatures above 420C significantly reduces irradiation hardening of some types of
steel. In a 16 mA beam, this window could be 0.045 mm thick and still maintain the
same operating temperature. There would now be a safety factor of 1.78 in the window’s
thickness.
Inconel-718’s mechanical behavior in a 16 mA beam was discussed in the beginning of
the Materials- Maximum Possible Flux section. Because of the difficulty of making
Nickel-based windows thin, I will state the 16 mA behavior of the Nickel window that
was thickest to begin with. Kubota KHR48N can tolerate 32.7 mA at 0.045 mm of
thickness and an operating temperature of 760C. There is no safety due to long lifetime
data. In a 16 mA beam, this window could be 0.092 mm thick and would have a safety
factor of 2.04.
A Nb-20W-7Ti-3Mo-1Zr window can tolerate roughly 126 mA of beam current at 0.043
mm thickness and an operating temperature of 1200C. In a 16 mA beam this window
could be 0.339 mm thick and maintain the same operating temperature. There would be a
safety factor of 7.88 in window thickness in addition to the factor of 4 safety already
there to account for a lack of lifetime data. In a 32 mA beam the window could be 0.169
mm thick with a safety of 3.94 in addition to the factor of 4 already there.
A Moly-TZM window can tolerate 202 mA at 0.036 mm of thickness and 1316C. In a
16 mA beam this window can be 0.455 mm thick and remain at the same operating
temperature. This thickness, 0.455 mm, can be produced by commercial methods and is
very stiff: There is an sample of 0.5 mm pure Molybdenum in the WPI Physics
Department at the time of this writing. With 0.455 mm of thickness, there is now a safety
factor of 12.6 in the window, in addition to the factor of 4 that was already there.
Alternately, a 32 mA beam could have a 0.227 mm window and a factor of 6.31
additional safety. This kind of flexibility also allows for some flaws in the initial
assumptions (Section 1). For example, even if emission cannot be made to reach 90% of
blackbody, there is room for the window’s thickness, and therefore heating, to be
reduced.
A Ta-10W window could possibly tolerate 80 mA at 0.123 mm thickness and 1600C for
an unknown but probably limited period of time. This thickness could be increased to
0.615 mm in a 16 mA beam, which would put an additional safety factor of 5 in the
window.
A Thoriated Tungsten window can tolerate 208 mA of beam current at 0.078 mm and
1927C. In a 16 mA beam this window could be as thick as 1.01 mm without running
any hotter or taking any more power from the beam. (Power loss to window is ~0.5% in
this case, 75kW.) The additional safety factor gained by doing this would be 13.0.
Alternatively, a 0.507 mm window could work with a 32 mA beam and a factor of 6.49
safety. Since it is possible and common to make WThO2 thinner than 1mm, the WThO2
window in a 16 mA, power-generating ADS could be made thinner and run significantly
below capacity. In this way it is similar to Moly-TZM, and has similar flexibility in
initial assumptions.
The Rhenium window was already well-suited to a 16 mA beam at 1600C in Section
2.2. If run at 2200C, it can be 0.891mm thick and take 26.7 mA of current. At this
temperature, it could be 1.49 mm thick in a 16 mA beam. This makes for an additional
safety factor of 1.67.
Conclusions: Thoriated Tungsten and Moly-TZM make the mechanically best refractory
ADS beam windows. Low-temperature, oxygen-tolerant windows must be thinner, and
are limited by the difficulty of manufacture. For this reason a steel window may come
out ahead, although the Vanadium alloy has technically more tolerance for flaws in the
initial assumptions.
The ability of these materials to withstand or anneal radiation damage remains to be seen.
Pure Vanadium was tested for radiological effects in the Experimental section.
Section 5: Power Generation
The assumption that a 16 mA beam is sufficient for power generation is justified here.
Assume:
1. Each proton from the beam will spallate 1 target nucleus and yield 30
neutrons. The actual number of neutrons per spallation event is a spread that
depends on the target material and proton energy, assumed here to be 1 GeV.
2. There is a reactor core which, without the neutrons produced by spallation, is
at 97% criticality. The spallation neutrons bring it to exactly 100% criticality.
This means that at any instant, 3% of the free neutrons are from spallation.
3. Each neutron that causes a fission event releases 200 MeV of energy. Again,
the actual energy is a spread that depends on fuel material, but 200 MeV is a
commonly used number8.
4. The beam is running at 16 mA, or 1017 protons/second total flux. Since these
are 1 GeV protons it is a 16 MW beam. The beam is 15% power-efficient. The
power plant has 30% thermodynamic efficiency. The system must be able to
tolerate miscellaneous loses that bring nuclear efficiency as low as 80%.
Calculations:
1. (30 free neutrons/proton)  (1017 protons/second) / (0.03) = 1020 free
neutrons/second
2. At least 80% of these cause a fission from which the energy can be captured.
0.80 fissions / neutron × 200 MeV/fission × 1020 neutrons/second = 1.6 × 1022
MeV/second.
3. Plant is 30% efficient: 0.30 × 1.6 × 1022 MeV/s × 1.6 ×10-13 J/MeV = 770
MW.
4. 770 MW produced – 16 MW / 0.15 power to the beam = 660 MW
Some math done on an electric bill shows that a house can be run on an average of a kW
of power. If a third of power consumption is residential this 16 mA ADS is capable of
powering a small-to-midsize city.
References for Sections 1-5:
[1] P. Vladimirov, A. Moslang, J. Nucl. Mater. 1-3 (2006) p. 287-299
[2] Isotopes Project: Stopping Powers. http://ie.lbl.gov/interact/abs3c.pdf
[3] L.K. Mansur, J. Nucl. Mater. 1 (2003) p. 14-25
[4] X. Jia, Y. Dai, M. Victoria, J. Nucl. Mater. 1 (2002) p. 1-7
[5] H. Nakashima, Radiological Safety for the J-PARC Project (2006), p. 29
http://eurisol.wp5.free.fr/WP5/Documents/5th_meeting_Munchen_2006/JPARC.pdf
[6] NIST Center for Neutron Research: http://www.ncnr.nist.gov/resources/n-lengths/
[7] NASA Technical Note Stress-Rupture and Tensile Properties of Refractory-Metal
Wires at 2000F and 2200F (1093C and 1204C) by Petrasek and Signorelli, Lewis
Research Center, 1969
[8] Krane. Intro. to Nuclear Physics, Wiley, 1988
+ In-line References.
Section 6: Experiment- Irradiation Hadening in Vanadium
Abstract
Many metals undergo hardening in the presence of radiation. Irradiation hardening
initially leads to increased tensile strength, but eventually to brittleness. This has been a
problem in ADS prototypes. The purpose of this experiment was to see if irradiation
hardening could be observed in Vanadium. Samples that had been irradiated in WPI’s
Washburn reactor and unirradiated samples were measured for Knoop hardness. Data
taken suggests that irradiation hardening did occur in the irradiated samples. The
unirradiated samples had a mean microhardness of 151  2 HK. The irradiated samples
had a mean microhardness of 157  3 HK when a very outlying data point is included,
and a mean microhardness of 160  2 HK when that point is excluded. In the first case,
statistical variation could be responsible for the irradiated vs. unirradiated hardness
difference 6.6% of the time. When the outlier is excluded, statistical variation could only
produce this difference less than 0.2% of the time. This suggests that the hardness
difference is statistically significant, and that Vanadium may be too sensitive for use in
an ADS beam window.
Introduction
The phenomenon of irradiation hardening has been observed in many metals, including
steel1, tungsten2, tantalum3, niobium3, and nickel4. The swelling, transmutations, and
dislocations that cause hardening would seem to be possible in all metals, given sufficient
radiation. Some metals are more susceptible than others. For example, a small amount
of rhenium improves the swelling resistance of tungsten at least up to 1073K [2]. It is
not desirable that an ADS beam window material be overly sensitive to radiation of any
sort. Even if not inside the core, damage from the proton beam can produce many free
neutrons, alphas, betas, and gammas. A material that showed mechanical changes after
small radiation exposures is probably not a good structural material where larger
exposures are expected.
Exposures that cause irradiation hardening may be expressed in several ways.
Sometimes damage is recorded, and expressed in terms of dpa, a difficult and obscure
unit to work with. Other times exposure is expressed in terms of the neutron flux per
square centimeter. This may be some 1020 n/cm2 [2,3]. The 10 kW Washburn reactor
cannot practically deliver this much neutron flux, at least not in the thermal range. Its
thermal flux is about 1011n/cm2/s [5]. An MQP poster by Christopher Patterson and
Timothy Tully, “Optimization of Thermal Neutron Flux in the WPI LEU Reactor Core”
suggests that there is much more fast neutron flux (Fig.1). However, the fast neutrons
may not contribute significantly to radiation damage, as they do not absorb well and
could not knock a metal atom out of its lattice unless extremely energetic. The gammaradiation in the core is about 106 Roentgen/hr. Alpha radiation is a unmeasured quantity,
but certainly present. Beta radiation is also unmeasured, but it alone is visible: The
Cherenkov radiation it causes takes the form of blue light (Fig. 2). It is possible for all
these types of radiation to have structural effects on a material, but it is unknown how
much damage they each contribute. The reactor was operated by Steve Laflamme and
student assistants.
The microhardness of the irradiated and unirradiated vanadium samples were measured
using a Knoop hardness tester. The Knoop tester makes a small, diamond-shaped
indentation in the material being tested. The ratio of the force on the indenter and the
area of the indent gives the Knoop microhardness. The testing machine was operated by
Boquan Li.
Each sample vanadium sample was about 2.5cm  0.5cm  0.05 cm. The samples were
cut from a single sheet by Roger Steele. The sheet was documented as 99.7% pure
vanadium.
Figure 1. From “Optimization of Thermal Neutron Flux in the WPI LEU Reactor
Core” MQP poster by Christopher Patterson and Timothy Tully. The neutron flux
is graphed as a function of location in the core, with neutrons separated into 4
energy spectra: thermal and 3 fast. The image suggest the presence of many more
fast neutrons than thermal. Unfortunately, the lack of units labels or explanations
makes this data difficult to quantify.
Figure 2. The blue glow, called Cherenkov radiation, is evidence of beta particles
(fast free electrons) in the Washburn reactor. The area where samples are inserted
is glowing brightly.
Procedure
A single 5  5 cm, 0.5 mm thick sheet of 99.7% pure vanadium “foil” was obtained from
Sigma-Aldrich. This piece of metal was very stiff, not foil-like. There was some bluegreen oxidation on its surface, and many abrasion scratches. These scratches later made
hardness testing more difficult, and ought to have been polished off. The metal was also
not perfectly flat. Four appropriately-sized strips were cut from this sheet by Roger
Steele. Each took 15 to 20 minutes on a cutting wheel.
Figure 3. Uncut Vanadium.
The samples were brought down to the nuclear lab and weighed.
Table 1. Sample masses.
Sample 1
Sample 2
Sample 3
Sample 4
0.3625 g
0.4052 g
0.3603 g
0.4097 g
Samples 1 and 2 were selected for irradiation and put in small specimen jars. Sample 2
was put in the jar marked “D”. Samples 3 and 4 were visually distinguishable. The
samples were wiped but not washed beforehand.
The Washburn reactor was started shortly after 1:00 pm and was at full power by 1:42
pm. “Full Power”, according to the digital monitor, is 9600  100 W. The reactor
remained at full power throughout the irradiation. Pool temperature also remained fairly
constant at 76  1 F.
The samples were fed down into the core at 1:47 pm. They remained there for exactly an
hour, at which point the reactor was shut down by dropping the blades into the core.
After this hour, the neutron flux through them totaled about 3.6  1014 n/cm2. They had
been exposed to 106 Roentgen of gamma-rays. Their expected activity level was 106.3
mCi [5], far too hot to be removed from the pool. For this reason they were allowed to
remain in the pool until the next day. The half-life of radioactive 52V is 3.76 minutes, so
about 370 half-lives had passed when the experiment began again the next day.
It was apparent upon removing the samples from the pool that they were still hot. A
gamma intensity of 0.38  0.02 mR was measured, and the Geiger counter beeps were so
continuous as to overlap each other. Sample 1 was placed in the 8192-channel
Germanium-crystal gamma spectrometer. This spectrometer is known to have
background peaks corresponding to 40K (1463.03 keV), 214Pb (87.06 and 77.22 keV) , and
238
U (122.98 keV). Sample 1 showed 40K, and all 6 of the peaks corresponding to 187W,
which has a half-life of 23.9 hrs. From this it was determined that the unspecified 0.3%
impurity in the vanadium sample was significantly tungsten.
24
Na was also detected; it is
believed this came from handling the sample barehanded prior to irradiation. There was
a peak at 511.32 keV that was believed to be an “escape peak”, corresponding to the
mass-energy of the electron, and another at 2237.15 keV, which is the energy of an 24Na
peak minus the electron mass energy.
214
Bi is a natural decay product of uranium and
believed to be part of the background There was a lot of indeterminate noise in the
sample too, which could correspond to any number of elements. When reading these
spectrographs, it is on the researcher to determine which possible elements are plausible
[5]
An unirradiated V sample, Sample 3, was placed in the spectrograph as well to ensure
that no radioactivity had been present prior to irradiation. Surprisingly, radioactive 187W
Figure 4. Spectrograph of irradiated V sample, 22 hrs 43 min after completion of
irradiation. Note W impurities, underlined. Inset is background count. Numbers
given are energy in keV as recorded by the spectrograph. They are known to have a
calibration uncertainty of 1 keV near the center of the spectrum, but up to 8 keV
at higher energies. Generally less counts at higher energies because of the
inefficiency of the spectrometer there.
_____________________________________________________________
peaks showed there as well. When Sample 3 was placed in a different tray than Sample 1
had been in and counted again, 187W did not appear. This demonstrates the need for care
when dealing with radioactive samples, as they can contaminate the things they touch.
Because of the 187W activity and 24Na activity, the samples were not cleared for
temporary release from the facility until the next day, when they had had more time to
decay.
The next day Samples 1 and 2 were signed out of the facility. Their activity was now
estimated to be <0.1 μCi. They were brought upstairs to have their microhardness tested.
Unquantified uncertainty was introduced by the fact that the samples were not perfectly
flat and not polished. Since 1 and 2 could not be machined after irradiation, we made do
with the rough surfaces. The relationship of the surface scratches to the Knoop
indentation can be seen in Fig. 5.
There were 6 indents made on Sample 1, 4 on Sample 2, and 8 on Sample 3. It was
decided that results from Samples 1 and 2 should be taken as equivalent data, and that
there was no need to indent Sample 4, as its treatment was no different from that of
Sample 3. The results are given in Table 2.
Boquan Li, who operated the hardness tester, believed that the outlying point mentioned
in the abstract was a fluke due to the sample not being flat. It is marked with an asterisk
in the table. This point does lie 2.35 standard deviations from the mean, and more than
means Chauvenet’s Criterion for disregarding data. Two sets of statistical analysis were
done for the results of this experiment: One with the outlying point included, and one
with it excluded.
Figure 5. Optical micrograph of the surface of Sample 3, showing scratches and
Knoop indentation. The Knoop indentation is about 220 microns long.
_______________________________________________________________
Table 2. Knoop Hardness. There is an unknown visual uncertainty.
Sample 1, Irradiated
Sample 2, Irradiated
Sample 3, Unirradiated
#
HK
Indent length
#
HK
Indent length
#
HK
Indent length
1
134.8*
(no record)
1
163.4
208.6 μm
1
157.1
212.8 μm
2
163.0
(no record)
2
161.7
209.7 μm
2
140.2
225.2 μm
3
163.0
209.5 μm
3
151.9
216.4 μm
3
150.6
217.3 μm
4
149.8
217.8 μm
4
155.9
213.6 μm
4
154.7
214.4 μm
5
159.1
211.4 μm
5
147.1
219.9 μm
6
171.1
203.5 μm
6
148.6
218.8 μm
7
150.5
217.4 μm
8
155.9
213.6 μm
Analysis
Samples 1 and 2 were analyzed together as 9 or 10 data points, depending on whether or
not the outlier can be excluded. At first glance, it certainly seems that more hardness
variation is present in the irradiated samples. Nonetheless, the outlier is very far out.
The mean hardness of the irradiated samples is calculated at 157  3 if it is included
(mean HK*rad, rounded), and 160  2 if it is not ( mean HKrad, rounded). The standard
deviation of HK*rad is *(rad)= 9.6, and the standard deviation of HKrad is  (rad)= 6.3.
All analysis was done using the 1/(N-1) definition of , the standard deviation.
According to Chauvenet’s Criterion if the number of measurements, N, times the
probability of getting a measurement like the outlier is less than ½., then the data may be
rejected. The outlier is 2.35*(rad) from the mean, and the probability of getting a
measurement like this is (1 - 0.9812) = 0.0188, according to the chart in Appendix A of
[6]. N 0.0188 = 0.188 < ½ , so the point certainly meets the criterion. Nonetheless
calculations are done both with and without it.
The unirradiated measurements were more obedient. The mean hardness, HK0, was 151
 2; the standard deviation of the measurements, (0), was 5.1.
The difference between HK*rad and HK0 is, using the un-rounded numbers:
(157.33 – 150.59)  ( 3.192 + 1.822) = 6.74  3.76. Since 6.74 / 3.76 = 1.84, the
difference is outside 1.84, where  here represents the probability that this difference
could be obtained through random statistical variation. According to the chart in [7],
there is a 6.6 % chance of this, or equivalently, that it will happen one time in fifteen.
The difference between HKrad and HK0 is, using the un-rounded numbers:
(159.83 – 150.59)  ( 2.212 + 1.822) = 9.24  2.86. Since 9.24 / 2.86 = 3.23, the
difference is outside 3.23, where  here represents the probability that this difference
could be obtained through random statistical variation. According to the chart in [6],
there is less than an 0.2 % chance of this, or equivalently, that it will happen less than one
time in five hundred.
These results suggest that the difference in hardness is significant and that irradiation
hardening did occur.
Conclusions
The appearance of radiation hardening in this sample was not entirely expected, because
thermal neutron flux through these samples was about 3 105 times less than neutron flux
through samples cited as irradiation hardened2,3. One possible conclusion is that alphas,
betas, gammas, and fast neutrons do more damage to vanadium than was previously
thought. In the first three cases, ionization of sample atoms may be the culprit.
The probable presence of irradiation hardening after 1 hr in the Washburn reactor casts
doubt on vanadium’s suitability as an ADS beam window material, because the radiation
conditions in ADS are likely to be much more stringent. The exception would be if
vanadium is capable of annealing most radiation damage at its ideal operating
temperature of 500C (see Materials Section).
Suggestions for other experiments along these lines include:
1. The samples should be polished to a mirror-sheen and tested for flatness prior
to irradiation.
2. The experimenter should be familiar with the operation of a Knoop hardness
tester, and be able to use it without supervision. This will allow many more data
points to be collected.
3. In the case of statistically significant results, the irradiated and unirradiated
samples could be heated to see if the hardness difference was reduced by
annealing. This experiment would require special precautions because of the
possibility of radioactive material evaporating from the samples.
4. Other materials could be tested. In particular, alloy systems may not have
been studied.
5. The exact mechanisms of hardening could be studied.
References for Section 6
[1] Journal of Nuclear Materials
Volume 356, Issues 1-3 , September 2006, Pages 287-299
Vladimirov, Moslang. “Irradiation Conditions of ADS Beam Window..:”
[2] He, Tang, Hesegawa, Abe “Microstructural development and irradiation hardening
of W and W-Re…” September 2006. stacks.iop.org/NF/46/877
[3] Miller. Tantalum and Niobium, New York Academic Press, 1959
[4] Materials Science and Engineering A
Volumes 309-310, 15 July 2001, Pages 198-202
Rodney, Martin, Brechet. “Irradiation Hardening by Interstitial Loops…”
[5] Steve Laflamme, WPI Reactor Operator
[6] Taylor. Intro. To Error Analysis, 2nd Ed., University Science Books, 1997